Third Year Technical Report, Part 1 NCR 23-004-091 NASA Lewis Research Center Grant Number 23-004-068

MEASUREMENTS IN A LARGE ANGLE OBLIQUE JET IMPINGEMENT FLOW --

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prepared by

John F. Fosa, Associate Professor

Division of Engineering Research MICHIGAN STATE UNIVERSITY

PRICES SUBJECT TO &%GZ East Lansing, Michigan 48823

https://ntrs.nasa.gov/search.jsp?R=19740017690 2020-02-29T06:17:58+00:00Z

T h i r d Year Techn ica l Repor t , P a r t 1 NGR 23-004-091 NASA Lewis R e s e a r c h C e n t e r Gran t Number 23-004-068

MEASUREMENTS IN A LARGE ANGLE OBLIQUE J E T IMPINGEMENT FLOW

p r e p a r e d by

John F. F o s s , A s s o c i a t e P r o f e s s o r

Division of Engineer ing R e s e a r c h MICHIGAN S T A T E UNIVERSITY E a s t Lansing, Michigan 48823 January , 1974

Velocity and surface p r e s s u r e measuremcnls , in the flow field

of an obliquely impinging je t , and their interpretation a s regards the

governing mechanics and the aerodynamic noise generation charac ter i s t ics

of such a flow a r e reported. A computer controlled probe positioning

mechanism allowed the measurement of the velocity magnitude and direct ion

in the plane paral le l t o the plate. The mean velocity and Reynolds s t r e s s

components were recorded. Measures of the t e r m s in the momentum

equation reveal the charac ter of the p r e s s u r e gradients in the neighborhood

of the stagnation point. The effects of the stagnation s t reaml ine location

on the vorticity field and the "Vortex Sound" considerations of Powell [ 121

a r e discussed in relationship to the aerodynamic noise generation effects

of this flow.

TABLE OF CONTENTS Page

. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . Introduction 1

. . . . . . . . . . . . . . . . . . . . . . . . . 1 . 1 . Motivation 1 . . . . . . . . . . . . . . . . . 1.2. Oblique J e t Impingement 1

2 . Experimental Faci l i ty . . . . . . . . . . . . . . . . . . . . . . 3

2.1. Flow System . . . . . . . . . . . . . . . . . . . . . . . 3 2 . 2 . Data Acquisition System and Measurement Techniques . 5

. . . . . . . . . . . . . . . . . . . . 3 . The P resen t Investigation 6

. . . . . . . . . . . . . . . . . . . 3.1. Motivation and Scope 6 . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . 2 . Results 6 . . . . . . . . . . . . . . . . . . . . . 3.2.1. Documentation 6 3 . 2 . 2 . Charac ter i s t ics of the Large Angle Impingement . . . . . . . . . . . . . . . . . . . . . . . Flow Field 7 3 . 2 . 2 . 1 . Symmetry Charac te r i s t ics of the Flow n e a r . . . . . . . . . . . . . . . . . . . . . . the Surface 8 3 . 2 . 2 . 2 . The Turbulence F ie ld n e a r the P la te Surface . . . . 9 3 . L . 3 . Additional Charac te r i s t ics of the Large Angle . . . . . . . . . . . . . . . . Oblique Je t Impingement 10 . . . . . . . . . . . . . . . . . . . 3 . 2 . 3 . 1 . Stagnation Point 10 3.2. 3 . 2 . Radial Equation of Motion . . . . . . . . . . . . . . 11 3.3. Implications: The Production of Acoustic Noise . . . . 12

4 . Suggestions for Future Studies . . . . . . . . . . . . . . . . . 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . 5 . ~ o n c l u s i o n s 16

. . . . . . . . . . . . . . . . . . . . . . . . . . . 6 . References 17

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figures 33

NOMENCLATURE

nozzle d iameter , 1. 9 cm (0.75 in) fo r the present study

hot-wire voltage signal

curvature of the jet centerline

s ta t ic p r e s s u r e

cylindrical coordinates ( see F igure 2)

* . velocity components in the r , 8, z directions

inviscid velocity magnitude a t the exit of the jet

velocity vector

car tes ian coordinates (see F igure 2)

Greek Symbols

a inclination of the approach jet (see Figure 2)

0

k?

Superscripts

(-)

angle of the probe, angle of the s t reaml ine respectively, with respec t t o the rad ia l direction

difference of ( )

del (nabla) operator

kinematic viscosity

density

vorticity vector

t ime average

* Note, lower case velocity components signify both the mean and fluctuating velocity components a s designated by the superscr ip t .

1. 1N'I'HC)I)UC'I'ION

1. 1 . Motivation

The successful development of STOL a i r c r a f t requires l a rge lift

forces a t relatively low forward a i r c r a f t speeds. The proposed uti l iza-

tion of these a i r c r a f t will be to se rv i ce a i rpo r t s n e a r urban population

centers ; hence, i t i s important that this l if t augmentation be effected with

a sufficiently quiet propulsion scheme. The externally blown f lap (e. b. f. )

represents one of s e v e r a l configurations under consideration by the Na-

tional Aeronautics and Space Administration t o achieve the required low

speed lift charac te r i s t ics ; however, i t has a l s o been determined that

considerable acoust ic noise can be generated by the jet impingement flow

field associated with this configuration. The e. b. f . configuration and the

oblique jet impingement flow a s i t s laboratory o r fundamental counterpar t

a r e shown in F igure 1. Identification of the sou rces of this noise and the

development of techniques to l imit i t can best be achieved by a multi-

faceted r e sea rch program. Numerous studies by National Aeronautics

and Space Administration personnel and other r e s e a r c h e r s (a representa-

tive sample i s provided by references 1-4) have demonstrated charac te -

r i s t ic features of the acoustic generation. The r e s e a r c h project descr ibed

herein i s motivated by a different aspec t of the problem. Specifically,

it i s proposed to investigate and identify the basic mechanics of the oblique

jet impingement flow field. The p r e s s u r e and turbulent s t r e s s fluctuations,

which a r e responsible f o r the acoustic noise , resu l t f rom the dynamics of

the jet impingement flow. Although the relationship of the acoustic noise

generation to these fluid dynamic quantities i s quite subtle and complex,

a knowledge of the mean flow, the turbulent s t r e s s e s and the vorticity

charac te r i s t ics will provide pertinent background for theoret ical s tudies

of the acoustic charac te r i s t ics of the e. b.f. Similar ly , the aerodynamic

considerations of achieving a n attached flow on the suction s ide of the

flap requi re a knowledge of both the la rge and s m a l l angle jet impingement

flows a s the background information to adequately descr ibe the flow

through the flap gap.

1. 2. Oblique Je t Impingement

The mechanics of the shallow angle , oblique jet impingement flow

field have been successful ly infer red f rom comprehensive p r e s s u r e and

velocity measurements by Foss and Kleis [5]. A s u m m a r y of these

resul ts is presented below and the relationship to the present work i s

a l so noted.

The presence of the plate imposes a kinematic constraint on the

jet flow; namely, the mater ia l of the jet cannot penetrate the plane of the

impact surface. This requires that the jet curve upward to flow over the

plate and/or that i t spread la teral ly over the plane of the surface. Nor-

mal jet impingement involves only the la t te r response; the resu l t s of [ 5 ]

indicate that the jet response i s p r imar i ly a n upward curvature for s m a l l

angles (0 5 a s 12 degrees , s e e F igure 2 for the nomenclature). This

inferrence i s made possible by comparing the sur face p r e s s u r e i sobars

with a re ference curve. The z e r o i sobar curve and the contour which

represents the intersect ion of the 0. l u o isotach (uo = jet exit velocity)

and a n imaginary plane located a t the plate 's su r f ace a r e proportional in

width for the sma l l angle cases . Since the z e r o isobar contour is a

measu re of the dynamically significant jet width, this proportionality i s

interpreted a s a n absence of significant jet spreading.

An analytical development is presented in [ 51 which allows the

curvature K of the jet center* zm to be determined f r o m the sur face

p r e s s u r e measurements . The curva ture of the jet K(x) resu l t s f rom the

net effect of the p r e s s u r e up to that x location; hence, i t depends upon

the l a t e ra l a s wel l a s the longitudinal p r e s s u r e distribution. I t i s possi-

ble to compare the K(x) distribution with the center l ine p r e s s u r e d i s t r i -

bution p ( r , 0,O) and determine a measure of the equilibrium between the

center l ine and the total p r e s s u r e conditions. This comparison demonst ra tes

the relative effect of the two geometr ic pa rame te r s , specifically, the im-

pingement angle and the dis tance f rom the plate. By comparing the

spreading measu res with the K(x) vs p(r,O,O) m e a s u r e i t i s possible to

infer that 1 ) the s m a l l angle and s m a l l distance above the plate condition

does not demonstrate significant spreading but neither i s the cent ra l ** portion of the flow in equilibrium, 2 ) the la rge angle flows show systematic

spreading and a lack of equilibrium, and 3) the other two combinations a r e

observed fo r intermediate angles and displacements.

* r , 0 , e m i s the location of the vector which is the mechanical equivalent of the je t ' s momentum flux. ** The concept of equilibrium in this context i s more descr ipt ive than quantitative. Specifically, it r e f e r s t o the relat ive t rends between the maxima of the p(x, o ,o ) and k(x) curves and, i n addition, the genera l shape of the curves . The word equilibrium is t o connote whether the jet tu rns em-masse o r whether the center plane phenomena a s revealed by p(x, o , o) is significantly different f rom the turning of the en t i re jet a s revealed by the K ( x ) curve.

2

A comprehensive argument i s formulated in [ 51 which

demonstrates that vorticity effects a r e of p r imary significance in the

mechanics of the oblique impingement flow. The flow through a plane

normal to the s t reamwise flow i s considered to represent the effects of

vorticity t ranspor t of the original azimuthal vorticity of the approach

jet, the production of vorticity by the stretching and reorientation of the

mean velocity field and the flux of vorticity through the plane of the surface.

(The la t ter is a consequence of the sur face p r e s s u r e gradients. ) The

overal l details of this model will not be considered he re , the r eade r i s

r e fe r red to [ 51 ; also, the vorticity effects which a r e pertinent to the

acoustics problem a r e discussed by Foss [ 61 in a paper which i s a l s o

reproduced in Appendix B of the Third Annual and Fina l Report describing

the total r e s e a r c h program supported by Grant No. NGR 23-004-068.

The mechanics of the la rge angle impingement flow a r e m o r e

complicated than those for the shallow angle cases reported in [ 51 ;

however, many aspects of, and the basic framework for . the analysis

can be used f rom this ea r l i e r study. In addition, some relevant experi-

mental data i s available f rom Donaldson and Snedecker [ 7 ] and Westley,

et. al . [8] . Funk [ 91 has made use of pr ior analytical work to in te rpre t

the noise producing mechanism of the e. b. f . configuration. His in te rpre-

tation of the "scrunbing mechanism" 1s of par t icular in te res t and rs

discussea ~n a la ter section. Beyond this, there a r e no additions to the

ea r l i e r l i t e ra ture review presented by F o s s and Kleis [ 101 . It should

be noted that support fo r this work has been obtained f rom the NASA

Langley Research Center , Noise Control Section, Dr. J ay Hardin,

Grant Monitor, Grant No. NGR 23-004-091.

2. EXPERIMENTAL FACILITY

2. 1. Flow System

A schematic of the laboratory utilized for this study i s shown + in F igure 3. A large centrifugal fan (speed control t o - one percent) with

an induced flow 7. 5 in. pipe t e s t section and a large plenum chamber on

the p r e s s u r e s ide is available fo r this work. The 105 d iameter long pipe

i s used to evaluate the per formance of the hot wi re data acquisition

system by comparison with the universal fully-developed pipe flow resul ts

of Laufer [II] and by the absolute evaluation of the Reynolds s t r e s s t e rm I

(- p t ) from i ts l inear variation with respec t to radius and i ts magnitude

a s determined f rom the p res su re gradient in the pipe. Such a ~ r o c e d u r e

i s used to determine the prec ise (and operationally defined) angle between

the two wires of an x-wire a r r ay . Such a n evaluation scheme i s described

by Patel[lZ] . The oblique impingement flow sys tem is shown in Figure 'k a flexible duct connects the plenum chamber to the la rge diameter inlet

tube shown in the figure.

The design of the oblique jet impingement flow sys tem was con-

trolled by seve ra l pr imary contraints. The ability to position the probe

a t any r , 8 , z location and the ability to align the probe with the mean

velocity orientation in the r , 9 plane were considered essential . The

la t ter constraint p rese rves the accuracy of the calibration, for sma l l

pitch angles , s ince the probe i s calibrated a t z e r o yaw angle to the flow.

A t r ave r se sys t em, mounted on a lathe bed ca r r i age , with computer

controlled stepping motor drives i s available; i t was decided that this

unit would be used fo r the large angle oblique impingement flows. This

unit is capable of positioning the probe to within 0. 001 in. perpendicular

to the lathe bed, to within 0.001 in. in z and to within 0.5 degrees in the

r , O plane. The 'desired range o f 0 values could only be accounted for

by a relative angular motion of the je t with respec t to the lathe bed.

This has been accomplished by mounting the jet on a rotating support

such that i ts axis passes through ( 0 , 0 , 0 ) a t a n angle of rr/4 radians with

respect to the vert ical axis. The probe t r a v e r s e sys tem a l so required

the gea r box and stepping motors to be located directly below the measur-

ing point; hence, the probe i s supported on a U shaped holder. The

"length of the U" i s res t r ic ted by vibration and s t ruc tura l stiffness con-

s t ra in ts ; a value of 12 inches was a rb i t r a r i ly selected fo r this off-set

distance. Consequently, the impact plate i s in the form of a c i rcu lar

a r c with a radius of 10 inches f rom the "impact point" (0 ,0 ,0) to the

plate edge. A jet nozzle of 0. 75 in. in te rna l diameter was selected a s

a nominal s i ze to allow sufficiently la rge r /d values, before the plate

edge influences the data , and sufficient resolution for the z/d region of

interest .

2 . 2 . Data Acquisition System and Measurement Techniques

A Texas Instruments 960 A minicomputer i s the cent ra l component

in the data acquisition sys tem (see F igure 5). This unit is used to position

the probe a t the r , z values prescr ibed for the t r ave r se (e. g . , 1 3 data

points a t z = 0.05 d , 0 <- r<-4 in. ) by means of analog voltage signals used

to drive the stepping motors , to r eco rd the data fo r a prescr ibed time

period (e. g . , 60 second averaging t ime) and to orient the probe into the

mean flow direction of the r , O plane by a scheme which re l ies upon the

symmetr ic and approximately cosine response of a yawed hot-wire probe.

The probe is positioned a t f 45, t 30, t 15, and 0 degrees with r e spec t to

the presumed flow direction (the direction found in the previous reading

of the t r a v e r s e ) , and the s t reaming direction (Po) is calculated by the

following technique. The mean hot-wire response a t each of the seven

positions Ti ( p i ) , i s divided by the maximum voltage Emax. and the

apparant angle of the probe with respec t to the head-on condition (P.-Poi) 1

is calculated f rom the relationship

- Ei = cos (pi-poi). - - E

max

The voltage values f rom the hot-wire probe (or s ta t ic p r e s s u r e t ransducer )

a r e digitized and initially processed in the minicomputer such that subse-

quent processing will resu l t in the mean velocity and turbulence quantities - - 7 - 2 7 u U expressed in laboratory coordinates, viz. , ur , uQ, urn uQ,

Specifically, let e el , and e be voltage values f rom the hot-wire probe 0' 2

a s it i s oriented at Po and a t po + 45 degrees respectively.

where j is one sample of the digitized record (the digitized values a r e

formed a t the r a t e of 20 khz) and N is dependent upon the sampling t ime , 5 2 2 e2

e. g. N = 6 x 10 fo r a 30 second sample. f (e ) = eo, el , e Z , eo, e l , 2. k These values a r e recorded for specified t r ave r ses until sufficient infor-

mation i s recorded; the averaged values a r e then t ransfer red to the

IBM 1800 computer where the voltages a r e converted to velocities via

the response equations of the wi res and the fourth order polynomial used

to fi t the calibration, e = e(u) , of the "linearized" hot-wire probes. Two

mean velocity and three Reynolds s t r e s s t e r m s a r e known a t the given

point i n t e rms of probe coordinates ( s , t , z ) . The data can then he t rans-

formed to ( r ,@,z ) coordinates.

3. THE PRESENT INVESTIGATION

3. 1. Motivation and Scope

The motivation for the present study reported here in i s the

aforementioned acoustic and aerodynamic effects associated with the

externally blown flap. The relationship of this application problem to

the oblique impingement of a single axisymmetr ic jet on a la rge plane

surface, the lack of detailed information describing the mechanics of

the la t ter flow field and the a s ses smen t that a n appropriate initial study

would encompass detailed rad ia l velocity t r a v e r s e s with selected ver t ica l

t r ave r ses established the scope of the present investigation. The r e su l t s ,

presented below, support this a s s e s s m e n t of a n appropriate scope fo r the

investigation. That i s , sufficient information i s now available that a

comprehensive program can be identified to examine the appropriate

details of the large angle impingement flow field. The suggestions fo r

future studies a r e presented in the final section of this report .

3. 2. Results

There a r e two principal categories of resul ts derived f rom the

data of the present study; these a r e i ) documentation of the flow field and

i i ) character is t ics of the flow field a s infer red in the available data.

These two resul ts will be separately presented and discussed.

3. 2. 1. Documentation

The data representing the t ime mean sur face p r e s s u r e field

measurements have been collectively presented in the form of sur face

i sobars ; these a r e shown on Figure 6 (a). An expanded scale to bet ter

delineate the maximum p r e s s u r e region i s used in Figure 6 (b). The

length f rom the jet exit to the impact plate was seven d iameters and the

impingement angle was n/4 radians. These a r e the conditions for a l l of

the data reported herein.

The velocity field information was collected in three sepa ra t e

s e r i e s of data acquisition runs. Single wi re and fixed orientation t r a v e r s e s

were made in the jet pr ior to i t s impact on the plate and a l s o

downstream of th? geotnetric impact. poirlt. 'l'hesc data a r e shown in

Figure 7 . These resu l t s indicated that a local maxima in the velocity

occured near z/d = 0.053 (z = 0. 04 in,b Hence. this elevation was selected

a s the location of the plane for the radial t r ave r ses to define the velocity

field near the plate. A composite view of this velocity field i s presented

in F igure 8 . The ver t ica l velocity t r ave r ses to complete the exploratory \

documentation were taken a t r /d = 1 and r /d = 3 and a t the angles 0 = rr/4

and w/2. These resu l t s a r e presented in F igure 9 . In addition to the

graphical presentation, a listing of the data is provided in Appendix A.

As discussed below, the re i s reason to suspect the detailed values f rom

the .rr/3 and rr/6 radial t r a v e r s e s Hence,, these have been excluded f rom

the listing even though they a r e considered to be sufficiently accura te to

be included in the composite plot of F igure 8 . In order to complete the graphical documentation of the rad ia l

velocity t r ave r ses , i t was decided to adopt a presentation format which

would allow the relative importance of the various turbulence kinetic

energy production t e r m s to be assessed . These data a r e shown in 4. I

F igures 10 to 13. Since the radial t r ave r ses w e r e taken in even increments

( ~ r / d = 2/3) i t is possible to construct both radial and azimuthal plots

of the radial and azimuthal mean velocities, fluctuating velocity intensit ies

and fluctuating velocity correlat ion (kinematic Reynolds s t r e s s ) .

In order to faci l i ta te the comparison of the production effects,

the ver t ical ordinates were essentially maintained a t constant values for

a l l plots: The absc i s sa sca le for the radial t r a v e r s e presentations was

kept constant fo r all plots but i s a m o r e expanded scale than that used

for the azimuthal plots. The absc issa length i s cd~ltracted,approximately

50 percent for the azimuthal plots. Hence, the gradients .appear to be too

large by this factor. An additional rad ia l t r a v e r s e which makes use of a

somewhat f iner s e r i e s of probe locations and which is slightly c loser to

the plate is presented in F igure 14.

The azimuthal plots of the radial t r a v e r s e data revealed

apparant inconsistancies f rom the O = n/3 and rr/6 runs. Consequently,

these data were removed f r o m Figures 10 to 13 and the data listings

of Appendix A. They were utilized in the m o r e pictoral representat ion

of the velocity field presented in Figure 8.

3. 2. 2. Character is t ics of the Large Angle Impingement Flow Field

There a r e two principal charac ter i s t ics of the la rge angle im-

pingement flow which have been deduced from the data base represented

bv the results discussed above. The f i r s t character is t ic i s that the flow * field near the plate demonstrates two distinct "symmetry" pa t te rns ,

one i s "centered" near the location of the maximum surface p r e s s u r e

and the second i s a symmetry pa t te rn about the geometric intersect ion

of the jet axis with the plate and i s real ized when the flow reaches a

sufficiently la rge radial distance. The second character is t ic i s that the

turbulence kinetic energy in the region above the plate is not significantly

grea ter than that which can be accounted fo r by the convection of turbulence

energy by the mean motion. The data which allow the inference of these

two character is t ics and their significance for the generation of acoustic

noise and the aerodynamic phenomena of the externally blown flap con-

figuration a r e examined in subsequent sections.

3. 2. 2. 1. Symmetry Character is t ics of the Flow near the Surface

An overall picture of the flow pattern near the sur face of the

plate i s provided by combining the data f rom a l l of the rad ia l t r ave r ses

in such a manner that the magnitude and direction of the velocity in the

z/d = 0.053 plane i s revealed. This plot is presented i n F igure 8 . The symmetry "point" for the neighborhood of the maximum

pressu re i s approximately r /d = 0.87 (see Figure 6 (b)) and a 'rlocal

symmetry" of the JI (r , 0 ) field about this location i s suggested by the

data of the composite plot. Considerably more data in this region and

a m o r e sophisticated measurement technique, which i s capable of

segregating the r , 0 , and z velocity components, would be required to

improve the quantitative a s ses smen t of this flow pattern. The qualitative

observation of local symmet ry around the maximum p r e s s u r e region i s

expected to be supported by these additional measurements . As described

in a subsequent section, the present study was not extended to include

these measurements s ince a major modification to the flow and instrumen-

tation system is projected for the continuation study.

F o r sufficiently la rge r values (r /d 3 which represents a n

r / z value of approximately 55) the flow pat tern near the sur face evolves

* The word "symmetry" i s not meant to imply azimuthal independence of the velocity f ie lds , e .g . , a t a given r , Ur(o) >Zr(sr). The "symmetry point" i s ra ther like a non-axisymmetric source, loca$ion.

such that the geometr ic intersect ipn of the jet axis and the plate is the

symmetry "point1'. The rad ia l t r a v e r s e data for %/uo (see F igure 11) - demonstrates this effect quantitatively and the vanishing u,vg values (see Figure 1 2 ) f rom the s a m e t r ave r ses s imi lar ly confirm this obser -

vation. Theazimuthal variation of </u ( see F igure 12 ) shows that the 0

flow is not ax isymmetr ic about the symmet ry point (this i s not an expected

result since the jet inclination i s u/4, not rr/2 radians with r e spec t t o

the plate) but these distributions a l s o show that the variation with respec t

to 8 becomes r a the r slight a s r increases . It i s important to r e c a l l that

these results a r e for the region q u i t e c lose to the plate. The flow a t a

sufficient elevation above the plate will re ta in i ts predominant 8 = 0 orientation. The sur face velocity pat tern i s corroborated by the visuali-

zation studies of Westley, etc. al . [ 8 ] . The governing mechanics which resul t in these symmet ry patterns

a r e not fully revealed by these data. Without d i rec t measurements of

W ( r , @ ) and- and considerably m o r e comprehensive data , such an

assessment would not be feasible. However, the local symmet ry about

the maximum p r e s s u r e strongly suggests that the p r e s s u r e gradient i s

the dominant t e r m in the equation of motion for this region of the flow.

Some quantitative evaluations made possible by the extant data confirm

this speculation. These a r e presented in Section 3. 2. 3.

The effects which lead to symmetry about the geometr ic origin

a re much m o r e obscure. The su r face s tat ic p r e s s u r e field i s c lear ly

not symmetr ic about the origin and this would suggest that the local effects - - 2 leading to such symmet ry a r e the Reynolds s t r e s s e s , i. e . , u v and v g . r 9 It s eems c l ea r that the global symmetry of the ent i re jet i s involved in the

processes which lead to this result . However it i s not a s imple mat te r t o

connect the global effects to the Reynolds s t r e s s e s which mus t be responsible

for the local accelerat ions required to give the observed symmetry. One

mechanistic fea ture of the jet which has the potential fo r such a n effect is

the predominant azimuthal vorticity of the approaching jet.

3. 2. 2. 2. The Turbulence Field nea r the P la te Surface

The presence of the plate with the consequent no s l ip condition

and the strong velocity gradients might lead to the apr ior i expectation that

the turbulence energy level nea r the plate i s substantially g r e a t e r than

that to be expected if the plate w e r e absent. This expectation is not

supported by the data. Also, this observatien is relevant to the "scrubbing

mechanism" discussed by Fink [ 91 . 9

Figure 1 4 has been prepared a s a composite plot of the turbulence

intensity information f rom the radial t r ave r ses . In order to compare the

turbulence levels near the plate with the turbulence level of the jet i tself ,

the data for t11c condition z/d = 0.053 and 0 = 90 degrees has been plotted

on the same figure with tht: radial t r a v e r s e data of x/d = 6 and 8 , f r o m

Kleis and Foss C 131 . s e e Figure 16. This comparison appears t o be

the most reasonable basis f rom which to evaluate the relative turbulence

level created by the impingement process given the available experimental

data. However, it i s not unambiguous. A preferrable comparison would

be on the basis of a volume integral of the turbulence energy in a given

s t reamwise domain. Such an integral could be readily formulated f o r

the axisymmetr ic case but would require a n extensive s e r i e s of t r a v e r s e s

in the three-dimensional impingement flow. The vert ical t r a v e r s e data

of Figure 9 show that the turbulence intensity magnitudes in the plane

z/d = 0.053 is representative of the maximum values fo r these quantities

in the impingement flow albeit t he re i s a slight increase in the s teep

gradient (8cr/8z) region for z < 0.053d. F o r the present , the observation

that there i s not a significant excess of turbulence kinetic energy will be

used a s a guiding character is t ic and the enhanced production of acoustic

energy will be sought in t e r m s of other sources of sound generation.

This i s discussed in a la ter section.

The suppression of the turbulence intensity and the Reynolds s t r e s s e s

by concave curvature i s discussed along with numerous other effects a t

length by Bradshaw [ 141 . The present observations regarding the maximum

turbulence intensity values a r e compatible with these considerations. The

r. m. s. surface p r e s s u r e data of Westley, et. al . [ 8 ] indicate two maxima

located up and downstream of the origin. Apparently, these a r e related

to the stagnation point and to the local maxima in the turbulence intensity

magnitudes observed in the present data.

3. 2. 3. Additional Character is t ics of the Large Angle Oblique Je t Impingement

3. 2 . 3. 1. Stagnation Point

A technique of identifying the stagnation s t reamline by comparing

the measured velocity near the plates sur face with the sur face s ta t ic

p res su re taps was successfully employed by Foss and Kleis ,151 t o

demonstrate that the stagnation point is considerabley upstream of the

maximum p r e s s u r e location and near the z e r o sur face isobar fo r the

shallow angle impingementflow field. A necessa ry charac te r i s t ic of t h i s

technique i s that the s ta t ic p r e s s u r e a t the location of the velocity

measurement b e equal t o the a tmospher ic value. In the e a r l i e r study,

an over-pressure a t the velocity measur ing location would have resul ted

in a f a r the r upstream movement of the in fe r red stagnation point.

The s a m e technique cannot be applied to the measu remen t of the

stagnation point in the l a rge angle case . This r e su l t i s based upon the

following observations: i ) the loca l symmet ry of the velocity field ( see

3. 2.2. 1 ) requi res that the stagnation point be in the neighborhood of

x/d = -1 a n d i i ) comparing the su r f ace p r e s s u r e s i n this region with the

dynamic p r e s s u r e in fe r red from the jet velocity t r a v e r s e of F igu re 7 ,

the s ta t ic p r e s s u r e a t the location of the velocity measurement mus t be

grea te r than zero. Specifically, f r o m F igu re 7 , - 2 p ( r /d = 1 , 8 = rr) = P U o (0. 2) t Patm (3)

and from Figure 6(b)tk velocity magnitude i n this neighborhood of the

approaching jet i s of the o r d e r of 0 .3 uo. The stagnation p r e s s u r e for

such a condition i s given by -

Comparing the two equations, it i s apparan t that the s ta t ic p r e s s u r e a t the 2

measuring point mus t be of the o r d e r of 0. 15 p u . A s i m i l a r evaluation 0

of the stagnation p r e s s u r e i s possible using the data of the r ad i a l t r a v e r s e

a t z/d = 0.053; however , the c lo ses t data point to the suspected stagnation

point i s r /d = 1. 33. The recorded value i s u = 0. 179 u and this suggests 0

that the p r e s s u r e a long the stagnation s t r eaml ine a t this elevation i s of 2

the o rde r 0.185 p uo. Comparing these two approximate resu l t s supports

the presumed s t r eamwise p r e s s u r e var ia t ion along the stagnation s t r e a m -

line.

3. 2. 3. 2. Radial ~ ~ u a t i o ' n of Motion

The extant data allow a n examination of the t e r m s i n the r ad i a l

equation of motion nea r the stagnation point. The pertinent equation of

motion i s . . - Z r ve a; - -

- - r 2- a;: + -- i aurvg + a urW Ur FtFF t w - = - L % + v q u r a 7. p ar -(zr i-rae TZ (5)

2- = - F o r the region i n question, % 0 , 8;; /az = 0, v ry ur 0 , and urVO i j 0. r

.

a r e in b;tlanr.e and i t c'nn be a s s u n ~ ~ d that tho la t te r , for z > 0 , is less

than o r equal t u its v;i.loe a t the w;ill.

The quantities A and C can be e v a l ~ a t e d f rom Figure 14. They a r e ,

fo r r / d = 0.667,

A " -0.091

C " -1-0. 0215

F r o m the detailed isobar plot and using the arguments preceding (6).

t e r m D is approximated a s

D = -0.0308

Consequently, using these values , the "equation" would be

A - C - D = B

-0.091 - 0.0215 t 0.0308 = 0.0717

It i s in fer red f rom this evaluation that the rad ia l p r e s s u r e gradient a t

z/d = 0.04 i s much l a rge r than the s a m e quantity a t z = 0. This observat ion

suggests that the high p r e s s u r e of the stagnation point region extends above

the plate and that it i s re la t ively m o r e localized than at z = 0. That i s ,

if a n isobaric plot could be made a t z/d = 0.04 , then the contours would

be much c loser together than that shown in F igure (6b). Presumably , a

s i m i l a r phenomenon would be observed a t l a rge r distances f rom the plate. . .

3. 3. Implications: The Production of Acoustic Noise

On l t ~ o basis c r l the s l l i l l l~w angle impingement flow da ta , it has

been previously proposed by F o s s [ 6 ] that Powell 's "Vortex Sound"

a rguments a r e quite relevant t o the descr ipt ion of the noise produced by

the jet-plate impingement flow. The present resu l t s not only support

the s a m e interpretation for the la rge angle impingement c a s e , they a l s o

provide additional quantitative support fo r the relevance of such a model.

Powc:ll [ l 5 ] has t ~ t ~ o w t ~ 111:kt 1111: uirni1;trity 1,utwccn the dipole

effect (Ap a c r o s s the sur face a r e a s , which leads t o a corresponding

m a s s flux a c r o s s the plane of the sur face) and the circulation T, which

charac te r izes the s t rength of the vortex whose axis f o r m s the contour

bounding the a r e a , can be used t o develop a n express ion fo r the far f ie ld

velocity u@,t) a s *

where c is the ambient speed of sound and * signifies a delayed time. a

A schematic representat ion of this relationship i s shown in F igure 17.

This expression can be used to infer what propert ies of the vorticity in

the oblique jet impingement a r e m o s t important for the noise generation.

It should a l so be noted that arguments s imi lar to those referenced h e r e

have been used by Hardin [16 ] t o evaluate the acoustic charac ter i s t ics

of the orderly s t ruc tures in the turbulent jets.

As suggested by (7) the contribution to the acoustic no i se i s

f rom the unsteadiness with which the vortex loops change. (The solenoidal -

condition v . LC, = v . ( v x x ) = 0 requi res that the vorticity appear in

closed loops or terminate on the boundary of the flow. ) The azimuthal

vorticity of the approach flow will be distorted by the interaction with the

plate and the surface flux of vorticity wil l require a modification of the

vortex loop s t ruc tures within the jet field. When viewed f rom the ma te r i a l

coordinates of a portion of a given loop, the f i r s t t ime derivative of T s

can be expected t o be la rge fo r those loops which a r e elongated by the

interaction with the plate and/or f o r those loops in which significant

migration of the loop into new fluid occurs. The contribution to u b , t )

comes f rom the unsteadiness (i. e.. the magnitude of the turbulent

fluctuations) with which this occurs. These effects a r e shown schematically

in Figure 18.

The location of the stagnation s t reamline, which is important for

the qualitative discussion associated with Figure 18, has been approximately

identified from the sur face p r e s s u r e distribution and the velocity field

symmetry conditions a s discussed in Sections 3. 2. 3. 1 and 3. 2. 2. 1. This

location i s marked on the midplane velocity data t r a v e r s e of F igure 7.

F rom these considerations, i t is obvious that a quite significant amount

of the vorticity in the approach flow, i. e . , those loops which a r e

external to the = 0. 3u isotach cone, will be reformulated by the viscous 0

diffusion of vorticity. The requirement that this reformulation be

associated with viscous diffusion effects i s discussed a t length, along

with s imi lar considerations, in [ 6 ] . The diffusion effect i s briefly

considered he re fo r completeness; viz. , given the t ime mean vorticity

equation for the mater ia l e lements i n the 0 = o , ~ plane of the loop,

the only mechanism to al ter the sign of w i s the viscous diffusion t e rm. Y

These effects a r e , of course , quite important near the stagnation point.

It appears reasonable that thc qunntit:iLive magnitude of the

"reforn~ulation" contribution to the radiated sound i s much g rea te r , per

unit volume of the jet fluid, than the stretching effects which will occur

inside the = 0. 3 isotach cone. However, the total contribution to the

sound field i s not a s easily a s ses sed s ince the relative fractions of the

flow in which these two effects a r e important i s not obvious.

A detailed investigation of the stagnation region is suggested

by these resul ts . The plans f o r such a study are presented in the next

section.

4. Suggestions for Future Studies

The brief listing of suggestions fo r fur ther studies in this section

i s specifically related to the aerodynamic noise generation considerations

which have been the main focus of this study. These suggestions, there-

fore , a r e related t4,but a r e perhaps not identical with, the fur ther studies

which would be appropriate if the aerodynamics application was the

p r imary motivation.

Given the previous discussion of the "vortex sound" [ 6 , 141

considerations, two major a r e a s of interest a r e easily identified, namely,

i ) the stretching and deformation effects of the vorticity inter ior to the

s t r eam su r face which contains the stagnation s t reamline and ii) the details

of the vorticity field in the neighborhood of the stagnation point and the

reformulation of the axisymmetr ic vortex loops associated with the

stagnation phenomena.

It i s recommended that any experimental investigations of the

f o r m e r effects be coordinated with a significant analytical effort. The re

a r e two reasons for this recommendation: i) the governing equation fo r

the bulk of the vorticity in this region is somewhat s impler than the full

equation (the viscous diffusion t e r m can be neglected) and ii) the quantity

of data t o provide an "unguided" documentation of this three-dimensional

flow field is unreasonably la rge even fo r the computer aided acquisition

capability a s descr ibed in this report .

Conversely, the study of the flow field in the neighborhood of

the stagnation point i s quite compatible with a ra ther d i rec t experimental

approach. F r o m the resul ts of the present investigation, a new experimental

configuration is suggested in which thc nozzle diameter i s significantly

increased to allow the velocity maxima (z/d = 0.05) to be physically

moved away f rom the plate and hence to allow this region to be studied

in detail. Also, the construction technique of a fixed probe t r a v e r s e

axis and a movable jet does not appear to be compatible with the demands

for prec ise measurements in the stagnation point region. Hence, a

fixed jet and an additional degree of f reedom for the t r ave r se device

(x and y a s well a s z and 0 ) should be made available. The flow direction

measurement scheme described in Section 2 .2 appears quite adequate

and should be retained.

Soecific measurements should include data on the t r ansve r se

vorticity component, namely - - which i s feasible given 8 w

BE- adjacent x (ver t ical) and para l le l (horizontal) w i res to form the required

derivatives. (Note that an instantaneous evaluation of the derivatives

and their difference i s required to examine w ) The stagnation point t ' should be examined with independent techniques such a s t r a c e r s , velocity

direction measurements , and wall shea r s t r e s s indicators. The measure-

ments must allow fo r the (supposed) unsteady and obviously strongly

three-dimensional charac ter of the stagnation region. These charac ter i s t ics

make this investigation much m o r e complex than s imi lar investigations of

the stagnation region in axisyrnmetric o r plane flows.

Finally, i t would be beneficial t o modify the sur face p res su re

measuring configuration t o again allow the x-y coordinate evaluation of

p(x.y,o). Such data can be readily processed a s before, s e e F o s s and

Kleis [ 5 ] . t o revea l the t ra jec tory of the jet centerline (based upon the

momentum flux) and consequently the curvature of the centerline. Such

an arrangement would a l so allow fo r a f iner and m o r e regular gr id

spacing of the measurements in the neighborhood of the stagnation point.

The examination of the governing mechanics of the oblique jet

impingement can benefit f rom the extensive discussion by Bradshaw [14] of the

mechanistic fea tures of curvature effects on turbulence s t ructure. Also, this

serves to emphasize the complexity of the present problem. Specifically.

the curvature effects near the stagnation point will influence the turbulence

s t r e s s field which, along with the s ta t ic p r e s s u r e gradient and iner t ia l

effects , will determine the selection of the stagnation s t reamline. As

noted by Bradshaw, the mechanics of the normal jet impingement flow

a r e not well known. The oblique impingement flow i s , of course , a much

more complicated one.

1 5

5. Conclusions

The following conclusions a r e supported by the resu l t s of this

study.

1) The plane defined by z/d " 0.05 i s in the neighborhood of the

maximum velocity over most of the plate. Hence, this is a l so a plane

separating regions of opposite s e n s e vorticity. (Note that 8Gs/8z >> aiG/a~).

2 ) The flow in the z/d 2.0.05 plane (and presumably for sma l l e r

z/d values) can be character ized in t e r m s of two symmetry patterns.

Specifically, a local symmetry about the inferred stagnation point (x/d

-0.8) fo r the near region and symmet ry about the intersection of the jet

axis and the plate ( r /d = 0) fo r l a rge r radius values. The la t te r effects > a r e predominant for r /d w 3.

3 ) The maximum levels of the turbulent fluctuations in the region

near the plate a r e not la rger than the turbulence levels of the approach

jet. Insufficient data is available t o establish whether or not the jet / plate interaction resul ts in an increase in the total turbulence kinetic

energy.

4) Vortex sound considerations in combination with the identifi-

cation of the stagnation s t reaml ine in the sheared region (;;/Uo " 0. 3)

suggest that vorticity considerations a r e quite important regarding the

production of acoustic noise. The genera l charac ter i s t ics of the impingement

process suggest that the sur face vorticity field and the major reorientation

of the originally azimuthal vorticity field can be studied via a direct

experimental approach. The study of the less intense, but more volumet-

r ical ly more extensive, vorticity effects in the flow inter ior to the stagnation

s t r e a m tube should be guided by appropriate analytical considerations.

5) Quantitative est imates of the t e r m s in the equations of motion

indicate that significant ver t ica l and s t reamwise p r e s s u r e gradient effects

exis t in the neighborhood of the stagnation point.

6. References

1. Dorsch, R . C . , W. J. Kre im, and W.A. Olscn, "Exlernnlly- blown-flap noise ," Pape r 7L-129, Jan. 197L, AIAA New York, N. Y.

2. Putnam, T. W. and P. L. Lasagna, "Externally blown f lap impingement noise ," AIAA Pape r No. 72-664, 1972.

3. Haas, M. , "Blown flap noise , ' I MIT Report F T L 72-5. 1972.

4. Olsen, W. , J. Miles , and R. Dorsch , "Noise generated by impingement of a jet upon a l a rge f la t board," TN D-7075. 1972. NASA. Cleveland, Ohio.

5. F o s s , J. F. and S. J. Kleis. "The oblique impingement of an ax isymmetr ic jet , " Second Annual Report , NASA Grant NGR 23-004-068, December 21. 1972.

6. F o s s , J. F. , "Vorticity effects in oblique jet impingement flows a s a background fo r the acoust ics problem," Interagency Symposium on University Resea rch in Transportation Noise, edited by G. Banerian and K. Karamchet i , Vol. I, 273, Stanford University (March 1973).

7. Donaldson, C. DuP. and R. Snedecker, "A Study of f r e e jet impingement. P a r t 1. Mean proper t ies of f r e e and impinging je t s , " Journa l Fluid Mechanics , Vol. 45, p. 2, 1971.

8. Westley, R . , J. H. Woolley, and P. Brosseau , "Surface p r e s s u r e fluctuations f rom jet impingement on a n inclined flat plate," AGARD Sympossium on Acoustic Fatigue.

9. Fink, M. R. , "Mechanisms of external ly blown flap noise ," AIAA Pape r No. 73-1029, Oct. 1973.

10. F o s s , J. F. and S. J. Kleis, "A study of the round-jet/plane-wall flow f ie ld ," F i r s t Annual Report . Grant NGR 23-004-068

(October 197 1).

11. Laufer, J. ; "The s t r u c t u r e of turbulence in fully developed pipe flow," NACA Report No. 1174, 1954.

12. Pa te l , R. P., "Measurement of the Reynolds s t r e s s e s in a c i rcu lar pipe a s a means of testing a Disa constant-temperature hot-wire anemometer , " McGill University Technical Note 63-6.

13. Kleis, S. J. and J. F. F o s s . "The effects of exit conditions on the development of a n ax isymmetr ic turbulent f r e e je t , It Third Year Technical Report , Grant No. NGR 23-004-068 (1 974).

14. Bradshaw, P., "Effects of s t reamline curvature on turbulent f low," ACARD ograph No. 169, August 1973.

15. Powell , A . , "Theory of vortex sound," Journal Acoustical Soc. of A m . , 2, 1, 177-195, January 1964.

16. Hardin, J. C. , "Analysis of noise produced by an o rde r ly s t ruc tu re of turbulent je ts ," NASA 'TN D-7242, April 1973.

R A D I A L T R A V E R S E JET AT 0 DEGREES

Note: p i s in degrees; columns 4 - 9 are expressed as percentages

R A D I A L TRAVFRSE JET AT 15 DFGRFES

- ---- .

Note: p i s in degrees; columns 4 - 9 are0expressed as percentages

R A D I A L TRAVERSE JET AT 45 DEGREES

r/d z/d - *

P IVl/uo u J u 0

Note: p is in degrees; columns 4 - 9 are expressed a s percentages

R A D I A L T R A V E R S E J E T A T 90 DEGREES

Note: p i s in degrees; columns 4 - 9 are expressed a s percentages

V E R T I C A L TRAVERSE JET A T 0 DEGREES

Note: p i s in degrees; columns 4 - 9 are expressed as percentages

R A D I A L TRAVERSE J E T AT 1 3 5 DEGREES

Note: p i s in degrees; columns 4 - 9 are expressed as percentages

R A D I A L TRAVERSE J E T AT 1 8 0 DEGREES - r/d z/d P Iq/u0 ur/"O

Note: p i s in degrees; columns 4 - 9 are expressed a s percentages

R A D I A L TRAVERSE J E T AT 3 0 DEGREES

-

Note: p i s in degrees; columns 4 - 9 are expressed as percentages

R A O I A L T R A V E R S E J E T AT 60 D E G R E E S - r/d z/d P IVl/u, uF/u0

Note: p is in degrees; columns 4 - 9 are expressed as percentages

V E R T I C A L T R A V E R S E JET AT 90 D E G R E E S - - -2 2 -2 2 r/d z/d P Ivl/~, ur/"o ve /uO ur/uO ve /uo

Note: 13 is in degrees; columns 4 - 9 are expressed a s percentages

V E R T I C A L TRAVERSE JET AT 90 DEGREES - - --a 2 -2 2 r/d z/d P IVl/u, Ur/"o ve/uo ur/uo ve/uo

Note: p is in degrees; columns 4 - 9 are expressed as percentages

V E R T I C A L

P 0.0

0.0

0 .o

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

T R A V E R S E JET AT 0 D E G R E E S

Note: p i s in degrees; columns 4 - 9 are expressed as percentages

V E R T I C A L TRAVERSE J E T AT 45 DEGREES r/d z/d - -

P IVl/uo -2 2 -2 2

",/"O vo/uo ur/uO vo/u', 1.333 0.013 17.0

1.333 0.026 17.5

1.733 0.040 17.7

1.333 0.053 17.7

1.333 0.066 18.2

1.333 0.079 18.7

1.333 0.093 18.3

1.333 0.106 19.1

1.333 0.119 19.6

1.333 0.133 20.4

1.333 0.1Rh 19.8

1.333 0.239 20.1

1.333 0.293 22.0

1.333 0.346 22.1

1.333 0.399 24.3

1.333 0.453 25.6

1.333 0.506 24.5

1.333 0.559 26.8

1.333 0.613 23.3

1.333 0.666 27.2

1.333 0.719 28.0

1.333 0.773 27.0

1.333 0.826 25.3

1.333 0.879 24.4

1.333 0.933 25.3

1.333 0.986 24.7

1.333 1.039 24.0

Note: p is in degrees;

68.8

70.4

70.7

70.3

69.4

68.2

67.1

65.5

64.1

62.7

57.6

51.5

46.6

41.1

37.1

32.8

29.6

26.0

22.7

19.7

17.7

15.2

13.7

12.4

10.7

8.6

7.9

columns 4

65.8 20.1 2.59 0.77

67.1 21.2 2.41 0.65

67.3 21.5 2.14 0.62

67.0 21.4 1.90 0.61

65.9 21.7 1.73 0.59

64.6 21.9 1.57 0.60

63.6 2 1.4 1.46 0.61

61.9 21.4 1.36 0.62

60.4 21.5 1.29 0.65

58.8 21.9 1.24 0.67

54.5 18.6 1.13 0.69

48.4 17.7 1.13 0.69

43.2 17.4 1.13 0.68

38 -0 15.5 1.14 0.62

33.8 15.3 1.10 0.56

29.6 14.2 1.03 0.48

26.9 12.3 1.05 0.33

23.2 11.8 0.87 0.37

20.8 9.0 0.78 0.31

17.5 9.0 0.68 0.30

15.6 8.3 0.60 0.26

13.5 6.9 0.53 0.23

12.4 5.9 0 a46 0.18

11.3 5.1 0.38 0.15

9.6 4.5 0.31 0.10

7.8 3.6 0.23 0.13

7.2 3.2 0.19 0.11

9 a r e expressed as percentages

V E R T I C A L T R A V E R S E JET AT 4 5 D E G R E E S - - -2 2 -2 2 r/d z/d I3 m/uo ~ r / ~ o ve/u0 q u o ve/uo

Note: p is in degrees; c 9 are expressed as percentages

Figure 1. The externally blown flap configuration for STOL aircraft.

a. Side View

Figure 2. Nomenclature for the oblique jet impingement flow.

3 3

Control panel and Instrumentation

Cross section 40" high 60" wide

screens Contraction

(large angle oblique jet impingement ratio = 36 flow and traverse systems. ) Octagonal 4 U-Lock

circular pipe 7. 5" I. D. seamles s aluminum L/D = 105

Figure 3. Schematic of laboratory.

a inlet flow

3 inch diameter

,gure4. Large anvle iet i rn~ineement I Hot- wire

#"robe

- -~ - m - ~ ~ - - . * ~ ~ D~ ~ ~

Ilow facility. 0 . 7 5 i n c h a nozzle I v r

static taps I I

r ,€I, z coordinate s y s t e m aligned w. r. t. the jet, x , y, z aligned w. r . t. the lathe bed.

Ay dr ive (*0,001 in. )

power supply and control ler fo r stepping m o t o r s

control anemometer (constant temp

A-D Converter A - D Converter

F igure 5. Schematic of data acquisition facility.

3b

NOTE: 1 cm = 1 inch d = 0.75 i nch

8 = .rr

(a) Complete data set

Figure 6 . Surface pressure isobar contours. a = 45 degrees, ~ / d = 7, jet Reynolds number = 4. 8 x 104.

(P - patrn) Contours represent level curves of 100 2 p u A sin a

0

2 2 p u dA/p u A. A = 0. 809 taken from [5].

P Jet'

Figurebb. Expanded scale to show detail of the maximum pressure region.

A - location of

0 . - 0.35 0 .,SO 0 . 7 5 1 .O reference length for velocity scale

(41 ( 5 )

Figure 7. Velocity magnitude traverses in the 9 = 0. 0 = n plane.

-

-

-

-

-

- Note: data points a r e

located a t each - 0. 667d.

-

1 m

h 0 * u $ h 0

W

V1

: .* 4

OJ m m P

Figure 8. Composite view of the velocity field in the plane z/d = 0. 053.

4 Conditions ~ / d = 7, R = 4..8 x 10 , a = 45 degrees. e

Figure 9. Vertical velocity traverses.

I I 10 8 6 4 2 0

r/d b.)@ = 1 5 degrees

r/d . d. ) @ = 45 degrees

Figure 10. Radial t raverses of the radial velocity and the norm 1 Reynolds stress. (Presentation is to allow the magnitude of sf BTr/Br. )

. . . f . ' . 10 8 6 4 2 0

r/d c. 10 = 60 degreea

'/d f . ) @ = 90 degrees

h. ) = 180 degree*

c.)O = 30 depress

0.025 - - 2 u,ve/uo -

- - -

0 . 0 1 2 L

- - - -

I P 10 8 - 6

'/d

d. ) 0 = 45 degrees

Figure 1 1 . Radial traverses of the azimuthal velocity and the Reynolds shear stress . (Presentation i s to allow the magnitude of - u v air,/ar to be inferred. ) r e

r / d r/d a. 1 02 0 degrees b. ) Q= 1 5 degrees

1.0 O.llI:5-

+,'uo - L "?Y, /"" -

0 : G(,~L, - L -

= UrY, /u"

- -

0.5 0 . 0 1 1 L

- - - 6'

8 - m

I p 0

o 10 g - Y+-- 4 - - L

1.0 - , \u;" 0

0.5

o

r/d

e. ) b = 60 degrees

NOTE: The coordinate q ('I = [ re/d] l[rB/d] ) is arb i trar i ly d d i n e d reference such that r9/d,eferonce = 4-

, : , , : , : , O.b:Fo -

0 .04 0 . 0 1 0 ' 0.4--

- 0.0 0 . 0 0 5 0.2--

- 0 8 .

Figure 12. Azimuthal distributions of the radial velocity and Reynolds shear s tress . (Presentation is to allow the magnitude of - u,vg a 5 /a re to be inferred)

r

0

0.010

0

0

0.005 0

D

0 4 . 8 C 0 . I .2 . 3 .4 .5 .b .7

q 0 . l .2 3 4 .5 .b .7 .b

d.) r/d = 2.67 9 . ) r/d = 3 .33

0 * . I, I I I , , , ,

- , l l , , l l

0 . I . 2 . J .4 .5 .6 .7 .R . 9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

f . ) r i d z 4 . 0

-

0.2

0 n

..0.005

0

D D

0 * - a - - - - - 7 .; .I . . .b . .: .6 1.~0 1:l 1:2 i .3 1:4 1:' 1!6 1!7 ' h. ) */d = 5.33

i . ) ; 6.0

0 - A a - 0 D - a -

---q .I . 2 3 .4 . 6 7 . . 1 . 1.1 il2 113 114 115 i.6 1.7 1.8

j.) r/d = 6.67

0 A - . 0 . 0 a

0 .; .i . . . -

. .k ' 7 .fi 1!0 1l1 1.~2 1:s f.4 f.5 116 117 118 ' k.) r/d = 7.33

I.) r j d = 8.0

Figure 13. Azimuthal distributions of the azimuthal velocity an5the azimuthal Reynolds s t ress . (Presentation is to allow the magnitude of vg 8Ve/a re to be inferred. )

Note: The coordinate q (q [ re/d] /[ re/d] reference ) is arbitrarily defined such that

reference=4rr.

h . ) r / d = 5 . 3 3

0.2

0.0

- -0.005

0 = ? /" 0 0 * 0

0.2

0.0

f .; ".; .! .: :5 .! .; .; .f 1:O l!l :.2 1:3 ' ~ 4 :.5 1:6 1:7 ;.rn k.) r/d = 7 . 3 3

- 4 2

-0.005 b ' v0/u, . 0 = Te/u, . 0 i , .in . . .i .; .LB .$ ?o if1 1.B i> 1:4 ?s ;.6 1.7 1.8 1.9

1.) r/d = 8.0

NOTE: The coordinate 0 (0 = [re/dl /t re/dl peference) ie arbltrarlly defined

such that rB/d reference = 4-

- - Figure 14. U / U ~ and u /u vs r /d for the 6 = 0 plane, z/d = 0.04

0

(h/d = 7, jet Reynolds number = u d / v = 4.8 x lo4) 0

Scale: 2 cm = 1 i n

d = 0. 75 in

x oblique jet data a = 45, = 90, z/d = 0.053

t a 0 round jet data , x/d = 8 . round jet data, x/d = 6

Figure 16. Comparison of turbulence intensity m nitudues f rom a f r e e and the impinging jet flows. Note M = ( 3 u + c 2 ) / u 0 f o r the f r e e jet and (42 + G</ u f o r the oblique impingement flow. r o

(a ) Streamline flow pat tern based upon vortex loop with strength T.

(b) Dipole sheet adjusted to yield the s a m e flow field as in (a).

Figure 17. Terminology fo r Powel l ' s vortex sound analysis. (Adapted f r o m Figure 3 of [ 1 Z] . )

streamlines of the stream surface which contains the stagnation streamline

pathline of vortex loop

(side view) (front view)

(a) Vortex loop stretching "inside" the stagnation streamline.

(b) Vortex loop exterior to the stagnation streamline which is reconstituted a s a result of the surface vorticity flux.

Figure 18. Schematic r e resentation of vortex loop behavior which contributes to 9 the quantity d ( rs) /d t2 .